How MRI Works: Physics and Equations

1. The Role of Hydrogen Atoms

MRI relies on the presence of hydrogen atoms in the body, particularly in water molecules. These hydrogen nuclei (protons) are key to the MRI process. When exposed to a strong magnetic field, the protons behave like tiny magnets.

Hydrogen in the Human Body

The human body is mostly made of water, and water contains hydrogen atoms. These hydrogen nuclei act like little bar magnets because they have a magnetic moment due to their charge and spin.

Example: In the body, there are billions of hydrogen protons, each with its own magnetic moment.

2. Placing the Body in a Magnetic Field

The first step in MRI is placing the body inside a strong magnetic field (typically 1.5 to 3 Tesla). This field aligns the hydrogen protons.

Alignment with the Magnetic Field

When the body is placed in the magnetic field, the hydrogen protons align either with or against the magnetic field. The alignment process can be described mathematically by the Larmor equation.

The Larmor frequency is given by: \[ \omega = \gamma B \] where: - \( \omega \) is the angular frequency of precession (how the protons "spin" in the magnetic field), - \( \gamma \) is the gyromagnetic ratio (for hydrogen, \( \gamma = 2.675 \times 10^8 \, \text{rad/s/T} \)), - \( B \) is the magnetic field strength (measured in Tesla).

3. Applying a Radiofrequency (RF) Pulse

A radiofrequency (RF) pulse is applied perpendicular to the magnetic field. This pulse "knocks" the protons out of alignment with the magnetic field.

Flipping the Protons

The RF pulse excites the protons, causing them to flip from their lower energy state to a higher energy state. After the pulse is turned off, the protons will return to their original alignment with the magnetic field.

Example: It's like pushing a spinning top off balance with your hand (RF pulse) and then letting it spin back (relaxation).

4. Proton Relaxation: T1 and T2

After the RF pulse, the hydrogen protons undergo two types of relaxation: T1 (longitudinal relaxation) and T2 (transverse relaxation).

T1 Relaxation (Longitudinal Relaxation)

T1 is the time it takes for the hydrogen protons to realign with the magnetic field after being flipped. This process is called longitudinal relaxation because the protons return to their original alignment along the axis of the magnetic field.

The time for protons to return to their aligned state is called the T1 relaxation time.

T2 Relaxation (Transverse Relaxation)

T2 is the time it takes for the protons to lose their synchronization with each other. This is known as transverse relaxation. It describes how the magnetic moments of the protons gradually dephase, causing the signal from the protons to decay.

The T2 relaxation time describes how fast the protons lose phase coherence: \[ M(t) = M_0 \cdot e^{-t/T2} \] where: - \( M(t) \) is the magnetization at time \( t \), - \( M_0 \) is the initial magnetization, - \( T2 \) is the transverse relaxation time.

Example: Protons in fat will have a short T1 and T2, which means they relax faster compared to protons in water (brain tissue), which have longer T1 and T2 times.

5. Signal Detection and Image Creation

As the protons relax, they emit radiofrequency signals. These signals are detected by the MRI scanner and are used to generate images of the body’s internal structures.

Creating MRI Images

The MRI scanner collects the signals and processes them to create detailed images of the body. The signals from tissues with different T1 and T2 values produce different contrasts, allowing doctors to distinguish between different types of tissues.

Example: Water (brain tissue) has a long T1 and T2, so it appears bright on T2-weighted images and dark on T1-weighted images. Fat, with shorter T1 and T2, behaves differently in the images.

Conclusion: MRI and Proton Behavior

The fundamental physics of MRI involves manipulating the magnetic properties of hydrogen protons. The protons' alignment, flipping behavior due to RF pulses, and relaxation times (T1 and T2) are the key elements that make MRI a powerful tool for medical imaging.